For the buttercream, stir 150 ml milk, 75 g sugar and pudding powder until smooth. Bring 3/4 l milk to the boil, stir in the pudding powder and simmer for 1 minute. Place in a bowl, place foil directly on the surface.
Allow to cool for at least 4 hours at room temperature.
For the yeast dough mix 500 g flour, 1 pinch of salt and 125 g sugar in a mixing bowl, add 100 g butter in flakes and eggs. Warm 1/4 l milk lukewarm. Crumble yeast into it and dissolve it.
Pour into the flour mixture and knead into a smooth dough with the dough hooks of the hand mixer. Cover and leave to rise in a warm place for about 45 minutes.
In the meantime, melt 150 g butter in a pot. Add 200 g sugar, vanillin sugar and cream, bring to the boil while stirring. Remove from the heat and stir in the almonds. Leave to cool.
Grease a fat pan (deep baking tray; approx. 32 x 39 cm). Knead the dough with floured hands. Roll out on the fat pan and press to the edges. Let it rise again for about 20 minutes.
Preheat oven (electric cooker: 200°C/circulating air: 175°C/gas: level 3). Spread almond paste on the dough. Let it rise again for about 15 minutes. Bake in the hot oven for about 20 minutes. Let it cool down.
Quarter the yeast base. Cut each quarter horizontally. Whisk 500 g butter with the whisk of the hand mixer for 6-8 minutes until white-creamy. Stir the pudding through, adding it to the butter by the spoonful.
Spread the buttercream evenly on the 4 lower bases. Place almond lids on top and chill for at least 1 hour.